面向开集环境的去中心化联邦域泛化故障诊断方法

刘军豪; 李强; 高小永

doi:10.16383/j.aas.c260215

面向开集环境的去中心化联邦域泛化故障诊断方法

doi: 10.16383/j.aas.c260215 cstr: 32138.14.j.aas.c260215

刘军豪^1,,
李强^1,,
高小永^{1, 2,}

1.
中国石油大学(北京)人工智能学院北京 102249
2.
中国石油大学(北京)海南研究院三亚 572024

基金项目: 国家自然科学基金(22178383, 21706282), 北京自然科学基金(2232021), 中国石油大学(北京)科研基金(2462020BJRC004)资助

详细信息

作者简介:
刘军豪：中国石油大学(北京)博士研究生. 2024年获得中国石油大学(北京)学士学位. 主要研究方向为设备故障诊断与健康管理. E-mail: junhaoliu.cup@gmail.com

李强：中国石油大学(北京)博士. 2019年和2022年在四川轻化工大学分别获得学士学位和硕士学位, 2026年在中国石油大学(北京)获得博士学位. 主要研究方向为电潜泵故障检测与安全维护. E-mail: liqiang.cup@gmail.com

高小永：中国石油大学(北京)教授. 2007年获得中国石油大学(华东)自动化专业学士学位. 2014年获得清华大学控制科学与工程专业博士学位. 主要研究方向为石油石化过程智能制造. 本文通信作者. E-mail: x.gao@cup.edu.cn

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出版历程
- 收稿日期: 2026-03-31
- 录用日期: 2026-09-29
- 网络出版日期: 2026-10-21

A Decentralized Federated Domain Generalization Method for Fault Diagnosis in Open-set Environments

LIU Jun-Hao^1
,,
LI Qiang^1
,,
GAO Xiao-Yong^{1, 2
,}

1.
College of Artificial Intelligence, China University of Petro-leum (Beijing), Beijing 102249
2.
Hainan Institute of China University of Petroleum (Beijing), Sanya 572024

Funds: Supported by National Natural Science Foundation of China (22178383, 21706282), Beijing Natural Science Foundation (2232021), and Research Foundation of China University of Petroleum (Beijing) (2462020BJRC004)

More Information

Author Bio:
LIU Jun-Hao　Ph.D. candidate at China University of Petroleum (Beijing). He received his bachelor degree from China University of Petroleum (Beijing) in 2024. His research interests include equipment fault diagnosis and health management

LI Qiang　Ph.D. of China University of Petroleum (Beijing). He received his bachelor and master degrees from Sichuan University of Science & Engineering in 2019 and 2022, respectively, and his Ph.D. degree from China University of Petroleum (Beijing) in 2026. His research interests include fault detection and safe maintenance of electric submersible pumps

GAO Xiao-Yong　Professor at China University of Petroleum (Beijing). He received his bachelor degree in automation from China University of Petroleum (East China) in 2007, and his Ph.D. degree in control science and engineering from Tsinghua University in 2014. His main research interest is intelligent manufacturing for petroleum and petrochemical processes. Corresponding author of this paper

摘要

摘要: 故障诊断是保障工业系统安全稳定运行的核心环节. 传统诊断模型通常需要汇集多方节点数据进行集中训练, 存在原始数据泄漏风险. 尽管联邦学习能够在不共享原始数据的前提下实现协同训练, 但其往往依赖中央服务器进行参数聚合, 不仅存在单点故障隐患, 还给服务器端带来沉重的通信负担. 此外, 现有联邦故障诊断方法大多受限于闭集假设, 难以应对实际开集场景中存在的数据分布偏移与未知故障涌现等问题. 为此, 提出一种面向开集环境的去中心化联邦域泛化故障诊断方法. 具体而言, 首先构建基于节点相似度的动态拓扑更新机制, 通过自适应调整通信拓扑结构, 促进跨节点互补信息交互. 其次, 提出幅值–角度解耦的联合优化策略, 促进多源特征对齐并压缩已知类特征空间, 从而降低开放空间风险并提高跨域泛化能力. 最后, 基于特征重构误差构建样本级自适应阈值机制, 为每个样本生成个性化拒识边界, 实现未知故障类别检测. 在三个故障数据集上的广泛实验表明, 该方法的平均H_score达到93.9%, 综合诊断性能优于现有方法.
- 故障诊断 /
- 去中心化联邦学习 /
- 域泛化 /
- 开集识别
Abstract: Fault diagnosis is essential for the safe and stable operation of industrial systems. Conventional diagnostic models generally require data from multiple nodes to be aggregated for centralized training, posing a risk of raw data leakage. Although federated learning enables collaborative training without sharing raw data, it typically relies on a central server for parameter aggregation, leading to a single-point failure risk and a heavy communication burden on the server. Moreover, most existing federated fault diagnosis methods are based on the closed-set assumption and struggle with data distribution shifts and emerging unknown faults in open-set scenarios. To address these challenges, we propose a decentralized federated domain generalization method for fault diagnosis in open-set environments. First, we develop a dynamic topology update mechanism based on node similarity to adaptively adjust the communication topology and facilitate complementary information interaction across nodes. Second, we propose a joint optimization strategy based on magnitude-angle decoupling to align multi-source features and compress the known-class feature space, thereby reducing open space risk and enhancing cross-domain generalization. Finally, we develop a sample-wise adaptive thresholding mechanism based on feature reconstruction errors to generate sample-specific rejection boundaries for detecting unknown fault classes. Extensive experiments on three fault datasets demonstrate that the proposed method achieves an average H_score of 93.9% and outperforms existing methods in overall diagnostic performance.
- fault diagnosis /
- decentralized federated learning /
- domain generalization /
- open-set recognition

HTML全文

图 1 联邦域泛化架构((a)基于服务器的联邦域泛化; (b)去中心化联邦域泛化; (c)开集去中心化联邦域泛化)

Fig. 1 FDG architectures ((a) Server-based FDG; (b) Decentralized FDG; (c) Open-set decentralized FDG)

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图 2 OS-DFDG总体架构图

Fig. 2 Overall architecture diagram of OS-DFDG

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图 3 动态拓扑更新机制

Fig. 3 Dynamic topology update mechanism

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图 4 解耦联合优化策略((a)$ {\cal{L}}_{{\rm{hs}}} $; (b)$ {\cal{L}}_{{\rm{cen}}} $; (c)约束效果)

Fig. 4 Decoupled joint optimization strategy ((a) $ {\cal{L}}_{{\rm{hs}}} $; (b) $ {\cal{L}}_{{\rm{cen}}} $; (c) Effect of constraints)

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图 5 阈值对比((a)类级阈值; (b)样本级阈值)

Fig. 5 Threshold comparison ((a) Class-wise thresholds; (b) Sample-wise thresholds)

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图 6 数据采集实验台

Fig. 6 Test rigs for data acquisition

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图 7 OS-DFDG损失曲线

Fig. 7 {Loss curve of OS-DFDG

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图 8 各方法在C1任务上的混淆矩阵

Fig. 8 Confusion matrices of different methods on task C1

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图 9 OS-DFDG在C1任务上的t-SNE可视化

Fig. 9 t-SNE visualization of OS-DFDG on task C1

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图 10 样本级自适应阈值可视化

Fig. 10 Visualization of sample-wise adaptive thresholds

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图 11 $ \lambda_{{\rm{cen}}} $与$ \lambda_{{\rm{hs}}} $的敏感性分析(右图采用对数横轴)

Fig. 11 Sensitivity analysis of $ \lambda_{{\rm{cen}}} $ and $ \lambda_{{\rm{hs}}} $ (right panel: logarithmic x-axis)

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图 12 $ K_{{\rm{in}}} $的敏感性分析

Fig. 12 Sensitivity analysis of $ K_{{\rm{in}}} $

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图 13 $ T $的敏感性分析

Fig. 13 Sensitivity analysis of $ T $

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图 14 $ p $的敏感性分析

Fig. 14 Sensitivity analysis of $ p $

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表 1 各数据集运行工况表

Table 1 Table of operating conditions for each dataset

数据集	工况	工况详情
CWRU	A	负载: 0 hp, 转速: 1 797 rpm
	B	负载: 1 hp, 转速: 1 772 rpm
	C	负载: 2 hp, 转速: 1 750 rpm
	D	负载: 3 hp, 转速: 1 730 rpm
PU	E	扭矩: 0.7 N$ \cdot $m, 径向力: 1 000 N
	F	扭矩: 0.1 N$ \cdot $m, 径向力: 1 000 N
	G	扭矩: 0.7 N$ \cdot $m, 径向力: 400 N
BJUT	H	转速频率: 20 Hz
	I	转速频率: 25 Hz
	J	转速频率: 30 Hz
	K	转速频率: 35 Hz

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表 2 各数据集类别描述表

Table 2 Table of category descriptions for each dataset

数据集	类别	损伤详情	标签	数据集	类别	损伤详情	标签
CWRU	Nor	—	0	PU	Nor	—	0
	IRF	$ 0.007\,\;{\rm{in}} $	1		ORF	EDM	1
	IRF	$ 0.014\,\;{\rm{in}} $	2		ORF	EE	2
	IRF	$ 0.021\,\;{\rm{in}} $	3		IRF	EDM	3
	BF	$ 0.007\,\;{\rm{in}} $	4		IRF	EE	4
	BF	$ 0.014\,\;{\rm{in}} $	5	BJUT	Nor	—	0
	BF	$ 0.021\,\;{\rm{in}} $	6		MT	缺齿	1
	ORF	$ 0.007\,\;{\rm{in}} $	7		RC	齿根裂纹	2
	ORF	$ 0.014\,\;{\rm{in}} $	8		BT	断齿	3
	ORF	$ 0.021\,\;{\rm{in}} $	9		Wear	齿面磨损	4

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表 3 不同方法的功能对比

Table 3 Functional comparison of different methods

对比方法	隐私保护	去中心化	域泛化	开集诊断
M1 (OpenMax)^[32]	$ \times $	$ \times $	$ \times $	$ \checkmark $
M2 (FDDG)^[33]	$ \checkmark $	$ \times $	$ \checkmark $	$ \times $
M3 (FedDGMC)^[17]	$ \checkmark $	$ \times $	$ \checkmark $	$ \times $
M4 (FDG-CA)^[19]	$ \checkmark $	$ \checkmark $	$ \checkmark $	$ \times $
M5 (FedPD)^[34]	$ \checkmark $	$ \times $	$ \times $	$ \checkmark $
M6 (PD-FedOS)^[35]	$ \checkmark $	$ \times $	$ \times $	$ \checkmark $
M7 (FOSFD)^[36]	$ \checkmark $	$ \times $	$ \times $	$ \checkmark $
OS-DFDG (本文)	$ \checkmark $	$ \checkmark $	$ \checkmark $	$ \checkmark $

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表 4 CWRU、PU与BJUT数据集实验任务设置

Table 4 Experimental task settings on the CWRU, PU and BJUT datasets

任务ID	源域$ \to $目标域	源域已知类别集	目标域完整类别集	任务ID	源域$ \to $目标域	源域已知类别集	目标域完整类别集
C1	$ \{B,\; C,\; D\} \to A $	$ \{0,\; 4 \sim 9\} $	$ \{0 \sim 9\} $	P5	$ \{E,\; G\} \to F $	$ \{0,\; 1,\; 2,\; 4\} $	$ \{0 \sim 4\} $
C2	$ \{B,\; C,\; D\} \to A $	$ \{0 \sim 6\} $	$ \{0 \sim 9\} $	P6	$ \{E,\; G\} \to F $	$ \{0 \sim 3\} $	$ \{0 \sim 4\} $
C3	$ \{A,\; C,\; D\} \to B $	$ \{0 \sim 3,\; 7 \sim 9\} $	$ \{0 \sim 9\} $	P7	$ \{E,\; F\} \to G $	$ \{0,\; 2,\; 3,\; 4\} $	$ \{0 \sim 4\} $
C4	$ \{A,\; C,\; D\} \to B $	$ \{0 \sim 6\} $	$ \{0 \sim 9\} $	P8	$ \{E,\; F\} \to G $	$ \{0,\; 1,\; 3,\; 4\} $	$ \{0 \sim 4\} $
C5	$ \{A,\; B,\; D\} \to C $	$ \{0,\; 4 \sim 9\} $	$ \{0 \sim 9\} $	B1	$ \{I,\; J,\; K\} \to H $	$ \{0,\; 2,\; 3,\; 4\} $	$ \{0 \sim 4\} $
C6	$ \{A,\; B,\; D\} \to C $	$ \{0 \sim 3,\; 7 \sim 9\} $	$ \{0 \sim 9\} $	B2	$ \{I,\; J,\; K\} \to H $	$ \{0,\; 1,\; 3,\; 4\} $	$ \{0 \sim 4\} $
C7	$ \{A,\; B,\; C\} \to D $	$ \{0,\; 4 \sim 9\} $	$ \{0 \sim 9\} $	B3	$ \{H,\; J,\; K\} \to I $	$ \{0,\; 1,\; 3,\; 4\} $	$ \{0 \sim 4\} $
C8	$ \{A,\; B,\; C\} \to D $	$ \{0 \sim 6\} $	$ \{0 \sim 9\} $	B4	$ \{H,\; J,\; K\} \to I $	$ \{0,\; 1,\; 2,\; 4\} $	$ \{0 \sim 4\} $
P1	$ \{F,\; G\} \to E $	$ \{0,\; 2,\; 3,\; 4\} $	$ \{0 \sim 4\} $	B5	$ \{H,\; I,\; K\} \to J $	$ \{0,\; 1,\; 2,\; 4\} $	$ \{0 \sim 4\} $
P2	$ \{F,\; G\} \to E $	$ \{0,\; 1,\; 2,\; 4\} $	$ \{0 \sim 4\} $	B6	$ \{H,\; I,\; K\} \to J $	$ \{0,\; 1,\; 2,\; 3\} $	$ \{0 \sim 4\} $
P3	$ \{F,\; G\} \to E $	$ \{0 \sim 3\} $	$ \{0 \sim 4\} $	B7	$ \{H,\; I,\; J\} \to K $	$ \{0,\; 1,\; 2,\; 4\} $	$ \{0 \sim 4\} $
P4	$ \{E,\; G\} \to F $	$ \{0,\; 1,\; 3,\; 4\} $	$ \{0 \sim 4\} $	B8	$ \{H,\; I,\; J\} \to K $	$ \{0,\; 1,\; 2,\; 3\} $	$ \{0 \sim 4\} $

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表 5 主要超参数配置

Table 5 Main hyperparameter settings

超参数	数值	超参数	数值
$ \eta_{{\rm{stage1}}} $	$ 2\times 10^{-4} $	$ \eta_v $	$ 1\times 10^{-3} $
$ \lambda_{{\rm{hs}}} $	0.1	$ \lambda_{{\rm{cen}}} $	2.0
$ T $	10	$ T_{\max} $	100
$ E $	1	$ B_{{\rm{batch}}} $	64
$ R $	10.0	$ p $	99.99%
$ \gamma $	0.5	$ \beta $	10.0

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表 6 OS-DFDG模型详细网络架构

Table 6 Detailed network architecture of the OS-DFDG model

组件	层级	配置详情	组件	层级	配置详情
特征提取器($ G_{ f} $)	卷积模块1	Conv1d(1, 16, k=64, s=1), BN, ReLU	VAE ($ G_v $)	全连接层1	Linear(512, 256), ReLU
	最大池化层1	MaxPool1d(k=2, s=2)		全连接层2	Linear(256, 128), ReLU
	卷积模块2	Conv1d(16, 32, k=16, s=1), BN, ReLU		潜变量层	Linear(128, 64) ($ \mu $ & $ \log\sigma^2 $)
	最大池化层2	MaxPool1d(k=2, s=2)		全连接层3	Linear(64, 128), ReLU
	卷积模块3	Conv1d(32, 64, k=5, s=1), BN, ReLU		全连接层4	Linear(128, 256), ReLU
	卷积模块4	Conv1d(64, 64, k=5, s=1), BN, ReLU		输出层	Linear(256, 512)
	自适应平均池化层	AdaptiveAvgPool1d(output_size=8)	回归器($ G_r $)	决策树数量	100
分类器($ G_c $)	全连接层1	Linear(512, 512), ReLU		决策树架构	节点: 50, 深度: 4
分类器($ G_c $)	全连接层2	Linear(512, $ M $)		学习率	0.05

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表 7 24个任务上的$ A_{{\rm{kn}}} $、$ A_{{\rm{unk}}} $和$ H_{{\rm{score}}} $对比结果(%)

Table 7 Comparison of $ A_{{\rm{kn}}} $, $ A_{{\rm{unk}}} $, and $ H_{{\rm{score}}} $ results on 24 tasks (%)

任务	M1			M2			M3			M4			M5			M6			M7			OS-DFDG
任务	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $
C1	80.7	90.9	85.5	76.4	99.0	86.2	82.9	95.0	88.5	73.6	87.9	80.1	95.4	100.0	97.6	87.1	89.1	88.1	90.2	82.5	86.2	92.9	97.7	95.2
C2	74.4	69.8	72.0	73.4	73.0	73.2	72.1	92.5	81.0	83.0	88.9	85.9	89.3	73.3	80.5	81.9	80.3	81.1	86.1	80.3	83.1	89.5	94.6	92.0
C3	97.7	99.9	98.8	90.4	100.0	94.9	99.3	100.0	99.7	98.3	99.9	99.1	91.3	84.9	88.0	94.7	94.9	94.8	96.2	99.7	97.9	99.3	99.8	99.6
C4	98.7	90.0	94.1	90.1	68.0	77.5	87.4	95.9	91.5	90.3	96.6	93.3	93.0	81.7	87.0	83.6	88.5	86.0	91.0	85.2	88.0	97.2	99.2	98.2
C5	90.8	99.2	94.8	89.7	89.5	89.6	99.8	97.1	98.4	96.4	86.2	91.0	96.5	95.6	96.0	98.4	97.0	97.7	95.5	88.2	91.7	99.0	99.7	99.4
C6	99.6	97.6	98.6	97.4	100.0	98.7	100.0	100.0	100.0	98.7	100.0	99.4	89.8	99.8	94.5	93.1	94.7	93.9	98.0	98.3	98.1	99.2	97.5	98.3
C7	83.3	100.0	90.9	88.5	99.3	93.6	92.1	100.0	95.9	91.5	95.3	93.4	89.5	92.0	90.7	74.9	92.7	82.9	90.8	89.6	90.2	99.1	92.4	95.7
C8	84.4	93.8	88.8	74.4	90.1	81.5	83.4	93.0	87.9	80.8	83.2	82.0	95.9	91.6	93.7	74.2	90.2	81.4	85.6	97.5	91.1	94.2	87.7	90.8
P1	94.6	100.0	97.2	99.2	93.5	96.3	97.4	89.6	93.3	95.9	80.1	87.3	93.3	100.0	96.5	93.0	100.0	96.4	88.6	99.9	93.9	97.8	99.8	98.8
P2	99.1	95.3	97.2	98.7	85.5	91.6	96.8	91.6	94.2	96.3	98.1	97.2	93.7	94.7	94.2	95.2	99.6	97.4	90.6	98.3	94.3	97.9	96.9	97.4
P3	99.1	99.1	99.1	99.4	97.6	98.5	98.3	99.1	98.7	83.6	100.0	91.1	67.5	82.6	74.3	90.5	92.7	91.6	90.8	99.2	94.8	96.1	97.6	96.8
P4	99.5	88.2	93.5	97.9	91.0	94.4	98.7	89.2	93.7	96.1	97.6	96.8	93.3	98.7	95.9	91.6	92.6	92.1	93.0	99.6	96.2	97.5	92.5	94.9
P5	93.8	98.0	95.9	97.4	89.9	93.5	94.7	99.8	97.2	95.7	94.0	94.8	98.1	97.7	97.9	91.1	98.0	94.4	88.4	98.7	93.3	99.1	97.6	98.4
P6	98.9	73.5	84.3	99.8	89.1	94.1	99.6	94.7	97.1	82.7	78.8	80.7	78.8	87.3	82.9	76.9	98.8	86.5	94.8	87.2	90.8	92.3	91.1	91.6
P7	84.0	94.1	88.7	74.9	100.0	85.7	76.6	96.1	85.2	90.8	96.3	93.5	90.6	89.7	90.1	74.6	82.6	78.4	76.5	95.3	84.9	94.3	99.0	96.6
P8	90.9	92.1	91.5	73.8	75.2	74.5	85.8	78.7	82.1	97.8	91.7	94.6	85.8	64.6	73.7	78.5	85.0	81.6	81.0	90.7	85.6	96.1	97.5	96.8
B1	86.4	79.2	82.6	70.1	95.8	80.9	71.2	98.2	82.6	92.2	77.2	84.0	86.3	83.8	85.0	79.4	91.8	85.1	73.7	86.4	79.6	81.2	90.0	85.4
B2	82.9	97.6	89.6	78.5	98.2	87.2	88.8	91.2	90.0	83.7	99.4	90.9	85.5	79.4	82.3	75.9	88.6	81.8	77.6	82.3	79.9	86.3	98.6	92.0
B3	95.4	91.6	93.4	93.7	99.8	96.6	91.4	100.0	95.5	90.9	93.4	92.1	94.9	88.6	91.6	89.5	90.6	90.1	94.3	80.2	86.7	96.2	99.8	97.9
B4	92.5	81.0	86.4	82.4	95.4	88.4	80.5	77.6	79.0	81.1	82.6	81.8	84.8	75.4	79.8	87.1	87.6	87.4	86.0	86.6	86.3	90.2	87.4	88.8
B5	84.4	89.0	86.6	85.9	85.2	85.6	89.2	84.4	86.7	86.2	91.8	88.9	95.7	83.6	89.2	77.1	95.8	85.4	89.9	78.6	83.9	90.7	90.2	90.4
B6	96.5	90.6	93.5	81.9	92.2	86.8	92.2	99.0	95.5	83.8	84.7	84.2	84.4	94.6	89.2	84.5	92.8	88.5	82.4	87.2	84.7	92.8	95.7	94.2
B7	76.5	89.0	82.3	64.1	83.0	72.3	71.9	91.1	80.4	63.8	81.0	71.4	63.2	82.2	71.5	63.3	92.2	75.0	63.4	78.2	70.0	66.3	88.0	75.6
B8	83.2	83.0	83.1	87.1	83.8	85.4	62.9	100.0	77.2	79.7	80.0	79.9	82.2	85.8	84.0	71.6	88.2	79.0	74.4	92.6	82.5	83.6	93.6	88.3
均值	90.3	90.9	90.3	86.0	90.6	87.8	88.0	93.9	90.5	88.0	90.2	88.9	88.3	87.8	87.8	83.6	91.8	87.3	86.6	90.1	88.1	92.9	95.2	93.9

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表 8 24个任务上的消融实验结果(%)

Table 8 Ablation results on 24 tasks (%)

任务	Ab1			Ab2			Ab3			Ab4			OS-DFDG
任务	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $
C1	97.4	92.3	94.8	90.5	95.2	92.8	79.2	66.4	72.2	80.5	96.3	87.7	92.9	97.7	95.2
C2	83.3	91.8	87.4	86.3	67.6	75.8	75.8	79.4	77.6	70.6	90.6	79.4	89.5	94.6	92.0
C3	99.8	83.8	91.1	99.5	88.8	93.9	89.9	78.0	83.5	98.2	100.0	99.1	99.3	99.8	99.6
C4	93.9	99.4	96.6	83.8	99.9	91.1	80.3	81.7	81.0	93.6	99.9	96.7	97.2	99.2	98.2
C5	99.8	94.1	96.8	99.6	86.7	92.7	80.5	98.2	88.4	95.0	95.1	95.0	99.0	99.7	99.4
C6	99.7	95.0	97.3	99.9	90.8	95.2	74.1	90.5	81.5	99.7	91.5	95.4	99.2	97.5	98.3
C7	99.5	85.7	92.1	96.8	84.0	89.9	76.3	79.8	78.0	87.1	85.9	86.5	99.1	92.4	95.7
C8	96.8	62.8	76.2	84.9	72.0	77.9	69.5	70.9	70.2	99.3	81.3	89.4	94.2	87.7	90.8
P1	92.0	99.9	95.8	100.0	95.4	97.7	99.9	76.1	86.4	100.0	92.7	96.2	97.8	99.8	98.8
P2	99.3	89.5	94.2	95.5	91.4	93.4	93.2	74.0	82.5	99.2	85.8	92.0	97.9	96.9	97.4
P3	89.5	93.9	91.6	88.9	90.8	89.8	85.6	99.0	91.8	81.6	99.4	89.6	96.1	97.6	96.8
P4	83.3	99.0	90.5	86.6	98.1	92.0	79.7	80.4	80.1	99.9	82.0	90.1	97.5	92.5	94.9
P5	90.1	98.7	94.2	97.0	91.0	93.9	90.4	80.9	85.4	99.7	87.0	92.9	99.1	97.6	98.4
P6	90.5	86.5	88.5	81.5	91.8	86.3	99.2	82.9	90.3	81.9	91.2	86.3	92.3	91.1	91.6
P7	88.4	99.1	93.4	90.2	97.8	93.8	67.2	86.8	75.8	91.0	99.7	95.1	94.3	99.0	96.6
P8	66.8	75.5	70.9	72.5	89.7	80.2	71.2	76.8	73.9	90.5	93.8	92.1	96.1	97.5	96.8
B1	84.4	79.0	81.6	79.2	88.4	83.6	77.3	77.4	77.4	71.5	94.8	81.5	81.2	90.0	85.4
B2	73.5	99.4	84.5	81.5	100.0	89.8	72.6	88.5	79.8	68.0	99.8	80.9	86.3	98.6	92.0
B3	78.0	79.2	78.6	93.3	99.4	96.2	74.9	99.8	85.6	79.2	100.0	88.4	96.2	99.8	97.9
B4	81.0	92.4	86.3	81.9	91.6	86.5	86.0	80.2	83.0	84.0	79.6	81.8	90.2	87.4	88.8
B5	88.5	83.6	86.0	89.2	81.8	85.4	89.6	83.0	86.2	77.9	87.4	82.4	90.7	90.2	90.4
B6	74.9	99.4	85.4	85.9	90.0	87.9	92.2	82.0	86.8	78.0	98.8	87.2	92.8	95.7	94.2
B7	61.4	87.4	72.1	67.6	84.2	75.0	51.0	70.6	59.2	81.5	62.0	70.4	66.3	88.0	75.6
B8	74.7	99.8	85.4	78.1	99.6	87.6	86.4	70.2	77.4	62.9	99.6	77.1	83.6	93.6	88.3
均值	86.9	90.3	88.0	87.9	90.2	88.7	80.9	81.4	80.6	86.3	91.4	88.1	92.9	95.2	93.9

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表 9 联合强连通性检验结果

Table 9 Joint strong connectivity verification results

数据集	节点数$ N $	固定入度$ K_{{\rm{in}}} $	$ q_{\max} $	$ B_g $
CWRU	10	2	4	31
PU	6	1	6	51
BJUT	10	2	3	21

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表 10 类别异质下的鲁棒性分析结果(%)

Table 10 Robustness analysis results under category heterogeneity (%)

场景	C1			P1			B1
场景	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $
同构场景	92.9	97.7	95.2	97.8	99.8	98.8	81.2	90.0	85.4
$ \alpha=1.0 $	93.0	94.6	93.8	98.0	94.0	96.0	73.8	97.8	84.1
$ \alpha=0.5 $	80.5	95.7	87.4	80.4	99.8	89.1	71.4	93.6	81.0
$ \alpha=0.1 $	67.4	98.7	80.1	71.6	91.2	80.2	66.7	94.6	78.2
类别缺失25%	73.5	79.0	76.1	73.0	99.5	84.2	72.2	99.6	83.7

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表 11 设备异构下的鲁棒性分析结果(%)

Table 11 Robustness analysis results under device heterogeneity (%)

设置	C1			P1			B1
设置	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $	$ A_{{\rm{kn}}} $	$ A_{{\rm{unk}}} $	$ H_{{\rm{score}}} $
同构场景	92.9	97.7	95.2	97.8	99.8	98.8	81.2	90.0	85.4
$ {\cal{H}}_{c}(0.2,\;0.4) $	92.5	94.7	93.6	94.8	97.3	96.0	89.3	79.6	84.2
$ {\cal{H}}_{c}(0.5,\;0.4) $	86.4	99.5	92.5	92.1	98.8	95.3	82.0	80.2	81.1
$ {\cal{H}}_{d}(0.8,\;0.2,\;0) $	96.9	87.0	91.7	98.4	92.7	95.5	87.8	76.4	81.7
$ {\cal{H}}_{d}(0.6,\;0.3,\;0.1) $	85.6	90.1	87.8	96.8	87.9	92.1	72.0	84.2	77.6

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